比较下面两个积的大小.(请写出比较过程)A=1.23456×6.56789B=1.23457×6.56788
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/20 17:41:13
![比较下面两个积的大小.(请写出比较过程)A=1.23456×6.56789B=1.23457×6.56788](/uploads/image/z/4872147-51-7.jpg?t=%E6%AF%94%E8%BE%83%E4%B8%8B%E9%9D%A2%E4%B8%A4%E4%B8%AA%E7%A7%AF%E7%9A%84%E5%A4%A7%E5%B0%8F.%28%E8%AF%B7%E5%86%99%E5%87%BA%E6%AF%94%E8%BE%83%E8%BF%87%E7%A8%8B%29A%3D1.23456%C3%976.56789B%3D1.23457%C3%976.56788)
比较下面两个积的大小.(请写出比较过程)A=1.23456×6.56789B=1.23457×6.56788
比较下面两个积的大小.(请写出比较过程)A=1.23456×6.56789B=1.23457×6.56788
比较下面两个积的大小.(请写出比较过程)A=1.23456×6.56789B=1.23457×6.56788
A=1.23456×6.56789=123456×656789 * 10^-10
B=1.23457×6.56788=123457×656788* 10^-10
有这样一个定律:两之和相同,两数越接近,两数积越大
123457+656788=123456+656789
656788-123457A
看不懂
A-B=1.23456×6.56789-1.23457×6.56788
=1.23456×(6.56788+0.00001)-(1.23456+0.00001)×6.56788
=1.23456×6.56788+1.23456×0.00001-1.23456×6.56788-0.00001×6.56788
=1.23456×0.00001-0.00001×6.56788
=0.00001(1.23456-6.56788)
=-0.00001×5.33332=-0.0000533332<0
所以A
A
=1.23456×6.56789
= (1.23457 - 0.00001) ×(6.56788 + 0.00001)
=1.23457 × 6.56788 + 1.23457×0.00001 - 6.56788 ×0.00001 - 0.00001×0.00001
=1.23457 × 6.56788 + 0.00001×(1.23457 - 6.56788...
全部展开
A
=1.23456×6.56789
= (1.23457 - 0.00001) ×(6.56788 + 0.00001)
=1.23457 × 6.56788 + 1.23457×0.00001 - 6.56788 ×0.00001 - 0.00001×0.00001
=1.23457 × 6.56788 + 0.00001×(1.23457 - 6.56788 - 0.00001)
=1.23457 × 6.56788 - 5.33332 × 0.00001
因为B = 1.23457 × 6.56788
所以A = B - 5.33332 × 0.00001
显然A 比 B大
收起